In a GP the first term is 5 and the common ratio is 2. The eighth term is

Options

A. 640
B. 1280
C. 256
D. 160

Answer

To find the eighth term of a geometric progression (GP) where the first term (A) is 5 and the common ratio (R) is 2, we can use the formula for the nth term of a GP:

\[ T_n = A \cdot R^{(n-1)} \]

### Step-by-Step Solution:

1. **Identify the values:**
- First term \( A = 5 \)
- Common ratio \( R = 2 \)
- Term number \( n = 8 \)

2. **Plug the values into the formula:**
\[ T_8 = 5 \cdot 2^{(8-1)} \]

3. **Calculate the exponent:**
\[ 8 - 1 = 7 \]
So, we have:
\[ T_8 = 5 \cdot 2^7 \]

4. **Calculate \( 2^7 \):**
\[ 2^7 = 128 \]
Now substitute this back into the equation:
\[ T_8 = 5 \cdot 128 \]

5. **Perform the multiplication:**
\[ T_8 = 640 \]

Thus, the eighth term of the GP is **640**.